The Nature of Mathematics

Lucy Dewan Yuliyanto

Department of Mathematics Education

Universitas Pendidikan Indonesia 

Abstract : There are plenty definitions about the nature of mathematics. Mathematics has no generally accepted definition, it’s caused background of mathematician, place, time and culture etc. The nature of mathematics is so meaningful, we can define math based on ethymology, ontology, axiology and ephistimology. Mathematics is science.

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hat’s mathematics? Somestimes, we can define it depend on social background, culture, time, philosophy, school of thought etc. It causes there are a lot of definition about the nature of mathematics. The nature of mathematics has been the focus of much writing over the last few decades (e.g., Begg, 1994, 2005; Dossey, 1992; Fuson, Kalchman & Bransford, 2005; Ocean, 2005; Presmeg, 2002; Winter, 2001). The nature of mathematics is explaining what the mathematics is from science view, knowledge view, onthology, ephistimology, axiology, its experts, the universality and many more. In this paper, we will discuss, research and tell about the nature of mathematics from experts’ opinions or views.

            The word of mathematics comes from latin mathematika and before that it’s from Greek mathema, it means knowledge, study, learning. It connects to mathein or mathenein (learning or thinking). Mathematics is doing mathematics, it’s practice, human activity. Practical mathematics has been a human activity for last thousands years. Rigorous arguments first appeared in Greek  mathematics, mos notably in Euclid’s elements. Mathematics continued to develop in Greece in 600 BC, in China in 300 BC, in India in AD 100, in Muslim world in AD 800, until now.

            Mathematics has no certainly definition. Different vew, school of thought, philosophy, place, time and expert, it’ll make different definition. These are several definition about the nature of mathematics from its experts. Aristotle defined mathematics as the science of quantity. 

 Abraham S Lunchins and Edith N Luchins (Suherman, 2001:17): “In short, the question what is mathematics? May be answered difficulty depending on when the question is answered, where it is answered, who answer it, and what is regarded as being included in mathematics.”

            There are people say that mathematics is language of symbol, numerical language. Mathematics is thinking way. Mathematics is logical thinking methods. Mathematics is the queen of science. Mathematics is the waiter of science. Mathematics is doing mathematics. Mathematics is solving problem. Math is structural science.

            Mathematics is organized from elements which are undefined, definitions, axioms, and theorem or postulates that is generally proved its truth, because of that, mathematics is usually called deductive science (Russefendi 1988 : 23). From material side, mathematics is abstract science (Gravemeijer, 1994). The view that mathematics is abstract is explained by Ernest (1991) and Ruseffendi (1979b). All mathematics is symbol logic (Bertrand Russell, 1903). The definition of nonspecialist reference works. Mathematics is the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects (Encyclopaedia Britannica).

            Mathematics is human activity (Gravemeijer, 1994), and mathematics is not about number, but about life Devlin (Darhim, 2004).

            Some learners and students think mathematics is difficult and boring. It’s agree with Russefendi’s opinion (1988) that mathematics is a lesson which is disliked by children. It’s something in common wit it, mathematics is something scare or very fightening and as much as possible to dodge. (Darhim, 2004).

Vakil (Darhim, 2004) in his book with the title “A Mathematical Mosaic” said, ... math is usefull tool, a haphazard collection of recipes and algorithms, a necessary prerequisite to understanding science. Mathematics as queen, not servent, of science. Math is uniquely aesthetic dicipline. Mathematicians use word like beauty, depth, elegance, and power to describe excellent ideas. In order to truly enjoy mathematics, one must learn to appreciate the beauty of elegant argument and then learn to construct them.

Mathematics is not only related with numbers and its operation, but also space elements as its target. However, showing quantity like that doesn’t fulfill the other objective of mathematics, that is showed to relationship, pattern, shape, and structure (Tinggih, 1972).

According to Muh. Fachrani’s opinion, the comprehensive view of mathematics : Mathematics is not arithmetic. Mathematics is problem posing and problem solving. Mathematics is the activity of finding and studying patterns and relationship. Mathematics is a language. Mathematics is a way of thinking a tool for thinking. Mathematics is a path to independent thinkng. Mathematics is useful for everyone.

            All in all, mathematics is an useful science that help us to solve problem, to think logically, and to do task structurally. Mathematics is great and amazing.

References

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Darhim. (n.n). Pergeseran Paradigma Pembelajaran Matematika Sekolah. File.upi.edu

Darhim. (n.n). Permainan Matematika Sebagai Latihan Untuk Menumbuhkan Minat Terhadap Matematika. File.upi.edu

Hudojo, Herman. (2001). Pengembangan Kurikulum dan Pembelajaran Matematika. Universitas Negeri Malang: Malang

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Nunez, Rafael. (nn). Embodied Cognition and The Nature of Mathematics : Language, Gesture, and Abstraction. Department of Cognitive Sceice UCSD

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Sharma, Sashi et al. (n.n). Students’ Perspectives on the Nature of Mathematics. University of Waikato 

Wikipedia.(2011). Quoted September 20^th 2011 from en.wikipedia.org : http:// en.wikipedia.org/definition_of_mathematics.htm